On lightcone string field theory from Super Yang-Mills and holography

TL;DR

This work probes holography in the pp-wave limit of AdS5×S5, arguing that the maximally supersymmetric pp-wave has a one-dimensional boundary that is naturally described by a quantum-mechanical matrix model built from the lowest KK modes on S3. It establishes a detailed dictionary between finite-time transitions in this matrix model (open and closed string sectors) and light-cone string amplitudes, with leading results showing agreement with supergravity expectations in controlled regimes and revealing when SYM dynamics are essential (notably for open strings). The analysis shows that nonplanar (1/N) and loop corrections can be organized in two finite parameters, a = gYM^2N/J^2 and b = J^4/N^2, providing a coherent perturbative expansion across holographic sectors, including splitting/joining and open/closed transitions. The paper also clarifies holography in the pp-wave via the Penrose limit, discusses extremal correlators, and points toward a nonperturbative, flat-space limit of string theory defined through SYM, with implications for giant gravitons and future explorations of contact terms and higher-point functions.

Abstract

We investigate the issues of holography and string interactions in the duality between SYM and the pp wave background. We argue that the Penrose diagram of the maximally supersymmetric pp-wave has a one dimensional boundary. This fact suggests that the holographic dual of the pp-wave can be described by a quantum mechanical system. We believe this quantum mechanical system should be formulated as a matrix model. From the SYM point of view this matrix model is built out of the lowest lying KK modes of the SYM theory on an $S^3$ compactification, and it relates to a wave which has been compactified along one of the null directions. String interactions are defined by finite time amplitudes on this matrix model. For closed strings they arise as in AdS-CFT, by free SYM diagrams. For open strings, they arise from the diagonalization of the hamiltonian to first order in perturbation theory. Estimates of the leading behaviour of amplitudes in SYM and string theory agree, although they are performed in very different regimes. Corrections are organized in powers of $1/(μα' p^+)^2$ and $g^2(μα' p^+)^4$.

Figures (17)

• Figure 1: a)Penrose diagram of Minkowski space represented as a patch of the Einstein static universe b)Penrose diagram of a 2d Minkowski space drawn in a plane. $\zeta \in (-\pi , \pi)$, since the original spatial coordinate is in $(-\infty, \infty)$. c)Penrose diagram of 4d Minkowski space represented in a plane. Each point represents a 2-sphere, except for $i^+, i^-$ and $i_0$. $\zeta \in (0,\pi)$ since the spatial coordinate is radial, hence positive. d)Penrose diagram of the patch of the pp wave conformal to Minkowski space, represented in 3 dimensions. Every point is an $S^7$, except for the 2 thick lines which represent the real boundary of the space. All other boundary points of the diagram are analytically continued over. e) Penrose diagram of the whole pp wave spacetime. It fills the whole Einstein static universe, except for the 1 dimensional null line which is its boundary. We have also the 2 disjoint points $i^+, i^-$ representing the timelike boundaries.
• Figure 2: Diagrams for splitting and joining amplitude
• Figure 3: Loop counting for splitting and joining of closed strings
• Figure 4: a)Regular 4-open-string vertex in the lightcone string field theory from SYM point of view. b)An open string emitting a closed string (lightcone string field theory vertex) from SYM. Thick lines represent quark propagators and thin lines adjoints.
• Figure 5: a) Open string breaking into two open strings. b)Two open strings reconnecting. c) closed string breaking into two closed strings. d) open string emitting a closed string. e) closed string breaking into an open string. We see that a) and e) are locally the same, and also b), c) and d) are locally the same.